LREE of a Dynamical Unstable D$p$-brane

TL;DR

This paper derives the left-right entanglement entropy for a bosonic Dp-brane with tangential dynamics, gauge fields, and tachyon fields, analyzing its behavior under tachyon condensation and thermodynamic laws.

Contribution

It introduces a method to compute the LREE for an unstable Dp-brane with complex background fields and examines its thermodynamic properties during decay.

Findings

LREE is computed for a Dp-brane with gauge and tachyon fields.

The behavior of LREE under tachyon condensation is analyzed.

Second law of thermodynamics constrains system parameters.

Abstract

We derive the left-right entanglement entropy (LREE) for a bosonic D$p$-brane. This brane has tangential dynamics and has been dressed by a $U(1)$ gauge potential, the Kalb-Ramond field and a tachyon field. For this purpose, the R\'{e}nyi entropy will be computed and then, by taking a special limit of it, the LREE will be obtained. Besides, the behavior of the LREE under the tachyon condensation process will be evaluated. In addition, after the transition of the system, i.e. the collapse of the unstable brane, the second law of the thermodynamics on the LREE will be checked. We find that preserving the second law imposes some conditions on the parameters of the setup.